【摘要】 目前的扫描体算法 ,只注重轮廓面的变形与参数描述 ,但对扫描过程中轮廓面与轨迹线相对位置变化没有考虑。为此本文提出一个新算法来改善扫描体造型技术 ,即采用几何变换理论 ,描述扫描体中的位移、旋转及广义变形。新算法与 Frenet法的比较结果显示新算法快速、精确更多还原

【Abstract】 A sweeping object in computer aided geometry design (CAGD) is determined by a profile surface(We call it “base surface”) and its trochoid. Existing methods for modeling complex sweeping object mainly focus on the deform and parameterization of profile surface. They do not take into account the change of the comparative displacement of profile surface and trochoid during the process of sweeping. We present a method to overcome this shortcoming. We can get the base surface of any spatial point in the trochoid by geometry transformation through the following three steps:①let the normal vector of the initial base surface be the same direction as that of the base surface to be obtained;②let these two normal vectors coincide through displacement and rotation;③make an inverse transformation of step 1. Through these steps, we can compute the displacement, rotation, and generalized deform of any sweeping object. Table 1 gives the comparison of our method with Frenet method when the base surface is a quadrilateral, or a pyramid. It shows that our method is fast and accurate.更多还原